A commutative ring in which any ideal has a primary decomposition, that is, can be represented as the intersection of finitely-many primary ideals. Similarly, an $A$-module is called a Lasker module if any submodule of it has a primary decomposition. Any module of finite type over a Lasker ring is a Lasker module. E. Lasker  proved that there is a primary decomposition in polynomial rings. E. Noether  established that any Noetherian ring is a Lasker ring.
|||E. Lasker, "Zur Theorie der Moduln und Ideale" Math. Ann. , 60 (1905) pp. 19–116|
|||E. Noether, "Idealtheorie in Ringbereiche" Math. Ann. , 83 (1921) pp. 24–66|
|||N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)|
Lasker ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lasker_ring&oldid=32341